ANN with MNIST
http://iai.postech.ac.kr/
Industrial AI Lab at POSTECH
Table of Contents
1. What's an MNIST?¶
From Wikipedia
- The MNIST database (Mixed National Institute of Standards and Technology database) is a large database of handwritten digits that is commonly used for training various image processing systems. The database is also widely used for training and testing in the field of machine learning. It was created by "re-mixing" the samples from NIST's original datasets. The creators felt that since NIST's training dataset was taken from American Census Bureau employees, while the testing dataset was taken from American high school students, NIST's complete dataset was too hard.
- MNIST (Mixed National Institute of Standards and Technology database) database
- Handwritten digit database
- $28 \times 28$ gray scaled image
- Flattened matrix into a vector of $28 \times 28 = 784$
More here
We will be using MNIST to create a Multinomial Classifier that can detect if the MNIST image shown is a member of class 0,1,2,3,4,5,6,7,8 or 9. Susinctly, we're teaching a computer to recognize hand written digets.
# Import Library
import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf
%matplotlib inline
Let's download and load the dataset.
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)
print ("The training data set is:\n")
print (mnist.train.images.shape)
print (mnist.train.labels.shape)
print ("The test data set is:")
print (mnist.test.images.shape)
print (mnist.test.labels.shape)
Display a few random samples from it:
mnist.train.images[5]
# well, that's not a picture (or image), it's an array.
mnist.train.images[5].shape
You might think the training set is made up of 28 $\times$28 grayscale images of handwritten digits. No !!!
The thing is, the iamge has been flattened. These are 28x28 images that have been flattened into a 1D array. Let's reshape one.
img = np.reshape(mnist.train.images[5], [28,28])
img = mnist.train.images[5].reshape([28,28])
# So now we have a 28x28 matrix, where each element is an intensity level from 0 to 1.
img.shape
Let's visualize what some of these images and their corresponding training labels look like.
plt.figure(figsize = (6,6))
plt.imshow(img, 'gray')
plt.xticks([])
plt.yticks([])
plt.show()
mnist.train.labels[5]
np.argmax(mnist.train.labels[5])
Batch maker embedded
x, y = mnist.train.next_batch(3)
print(x.shape)
print(y.shape)
- Our network model
- Network training (learning) $$\omega:= \omega - \alpha \nabla_{\omega} \left( h_{\omega} \left(x^{(i)}\right),y^{(i)}\right)$$
2.1. Import Library¶
# Import Library
import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf
2.2. Load MNIST Data¶
- Download MNIST data from tensorflow tutorial example
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)
train_x, train_y = mnist.train.next_batch(1)
img = train_x[0,:].reshape(28,28)
plt.figure(figsize=(6,6))
plt.imshow(img,'gray')
plt.title("Label : {}".format(np.argmax(train_y[0,:])))
plt.xticks([])
plt.yticks([])
plt.show()
One hot encoding
print ('Train labels : {}'.format(train_y[0, :]))
n_input = 28*28
n_hidden = 100
n_output = 10
2.4. Define Weights, Biases, and Placeholder¶
- Define parameters based on predefined layer size
- Initialize with normal distribution with $\mu = 0$ and $\sigma = 0.1$
weights = {
'hidden' : tf.Variable(tf.random_normal([n_input, n_hidden], stddev = 0.1)),
'output' : tf.Variable(tf.random_normal([n_hidden, n_output], stddev = 0.1))
}
biases = {
'hidden' : tf.Variable(tf.random_normal([n_hidden], stddev = 0.1)),
'output' : tf.Variable(tf.random_normal([n_output], stddev = 0.1))
}
x = tf.placeholder(tf.float32, [None, n_input])
y = tf.placeholder(tf.float32, [None, n_output])
2.5. Build a Model¶
First, the layer performs several matrix multiplication to produce a set of linear activations
Second, each linear activation is running through a nonlinear activation function
Third, predict values with an affine transformation
# Define Network
def build_model(x, weights, biases):
# first hidden layer
hidden = tf.add(tf.matmul(x, weights['hidden']), biases['hidden'])
# non-linear activate function
hidden = tf.nn.relu(hidden)
# Output layer
output = tf.add(tf.matmul(hidden, weights['output']), biases['output'])
return output
2.6. Define Loss and Optimizer¶
Loss
- This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.
- Classification: Cross entropy
- Equivalent to apply logistic regression
- Equivalent to apply logistic regression
Optimizer
- This defines how the model is updated based on the data it sees and its loss function.
- AdamOptimizer: the most popular optimizer
# Define Loss
pred = build_model(x, weights, biases)
loss = tf.nn.softmax_cross_entropy_with_logits(logits = pred, labels = y)
loss = tf.reduce_mean(loss)
LR = 0.0001
optm = tf.train.AdamOptimizer(LR).minimize(loss)
2.7. Define Optimization Configuration and Then Optimize¶
- Define parameters for training ANN
n_batch: batch size for mini-batch gradient descentn_iter: the number of iteration stepsn_prt: check loss for everyn_prtiteration
- Metrics
- Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the accuracy, the fraction of the images that are correctly classified.
Initializer
- Initialize all the variables
n_batch = 50 # Batch Size
n_iter = 5000 # Learning Iteration
n_prt = 250 # Print Cycle
sess = tf.Session()
init = tf.global_variables_initializer()
sess.run(init)
loss_record_train = []
loss_record_test = []
for epoch in range(n_iter):
train_x, train_y = mnist.train.next_batch(n_batch)
sess.run(optm, feed_dict = {x: train_x, y: train_y})
if epoch % n_prt == 0:
test_x, test_y = mnist.test.next_batch(n_batch)
c1 = sess.run(loss, feed_dict = {x: train_x, y: train_y})
c2 = sess.run(loss, feed_dict = {x: test_x, y: test_y})
loss_record_train.append(c1)
loss_record_test.append(c2)
print ("Iter : {}".format(epoch))
print ("Cost : {}".format(c1))
plt.figure(figsize=(10,8))
plt.plot(np.arange(len(loss_record_train))*n_prt,
loss_record_train, label = 'training')
plt.plot(np.arange(len(loss_record_test))*n_prt,
loss_record_test, label = 'testing')
plt.xlabel('iteration', fontsize = 15)
plt.ylabel('loss', fontsize = 15)
plt.legend(fontsize = 12)
plt.ylim([0, np.max(loss_record_train)])
plt.show()
2.8. Test or Evaluate¶
test_x, test_y = mnist.test.next_batch(100)
my_pred = sess.run(pred, feed_dict = {x : test_x})
my_pred = np.argmax(my_pred, axis = 1)
labels = np.argmax(test_y, axis = 1)
accr = np.mean(np.equal(my_pred, labels))
print("Accuracy : {}%".format(accr*100))
test_x, test_y = mnist.test.next_batch(1)
logits = sess.run(tf.nn.softmax(pred), feed_dict = {x : test_x})
predict = np.argmax(logits)
plt.figure(figsize = (6,6))
plt.imshow(test_x.reshape(28,28), 'gray')
plt.xticks([])
plt.yticks([])
plt.show()
print('Prediction : {}'.format(predict))
np.set_printoptions(precision = 2, suppress = True)
print('Probability : {}'.format(logits.ravel()))
You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of overfitting, when a machine learning model performs worse on new data than on its training data.
What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better...
$\Rightarrow$ As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will build a CNN and ultimately output a probability distribution over the 10 digit classes (0-9) in the next lectures.
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